Function Operations and Composite Functions

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

What are function operations?

Back

Function operations include addition, subtraction, multiplication, and division of functions.

Front

What is a composite function?

Back

A composite function is formed when one function is applied to the results of another function, denoted as (f ∘ g)(x) = f(g(x)).

Front

How do you find f(x) / g(x)?

Back

To find f(x) / g(x), divide the output of function f by the output of function g for the same input x.

Front

If f(x) = x^2 - 9 and g(x) = x + 3, what is f(x) / g(x)?

Back

f(x) / g(x) = x - 3.

Front

How do you find g(f(x))?

Back

To find g(f(x)), substitute f(x) into g(x) and simplify.

Front

If f(x) = -3x + 7 and g(x) = 2x^2 - 8, what is g(f(x))?

Back

g(f(x)) = 18x^2 - 84x + 90.

Front

How do you find f(g(x))?

Back

To find f(g(x)), substitute g(x) into f(x) and simplify.

Front

If f(x) = -3x + 7 and g(x) = 2x^2 - 8, what is f(g(x))?

Back

f(g(x)) = -6x^2 + 31.

Front

What is the result of f(n) - g(n) if f(n) = x^2 + 1 and g(n) = 2x - 5?

Back

f(n) - g(n) = x^2 - 2x + 6.